System and method for labeling maps

ABSTRACT

A system and method for label placement is disclosed that achieves the twin goals of practical efficiency and high labeling quality by employing cartographic heuristics. A caller defines map and label properties. Then labels are pulled within a map boundary. Labels are next ordered by priority in descending importance. The order of testing labels is determined. Attempts are made to move overlapping labels. This is an iterative process; therefore there must be criteria that halt the procedure. Upon reaching an acceptable solution, the label properties are adjusted to reflect the new label placements.

REFERENCE TO RELATED APPLICATION

This application is a continuation of U.S. patent application Ser. No.10/462,044, filed Jun. 16, 2003, now U.S. Pat. No. 7,425,968, the entirefile wrapper contents of which are hereby incorporated by reference asthough fully set out at length.

COPYRIGHT NOTICE AND PERMISSION

This document contains some material which is subject to copyrightprotection. The copyright owner has no objection to the reproductionwith proper attribution of authorship and ownership and withoutalteration by anyone of this material as it appears in the files orrecords of the United States Patent and Trademark Office, but otherwisereserves all rights whatsoever.

FIELD OF THE INVENTION

The present invention relates to a computer-implemented method andapparatus for automatically labeling maps or graph layouts in accordancewith predefined label criteria.

BACKGROUND OF THE INVENTION

Maps include geographic drawings showing countries, cities, rivers,bodies of water, mountains, and other features of interest. Labelingcartographic features is a fundamental part of map-making. Placing eachlabel optimally with respect to its corresponding feature invariablyproduces labels overlapping each other or too close to each other. Asthis results in confusion and unacceptable maps, methods to repositionlabels or not draw them at all must be used to create a map that conveysas much information as possible.

Tagging graphical objects with text labels is a fundamental task in thedesign of many types of informational graphics. This problem is seen inits most essential form in cartography, but it also arises frequently inthe production of other informational graphics such as scatter plots.The quality of a labeling is determined essentially by the degree towhich labels obscure other labels or features of the underlying graphic.The goal is to choose positions for the labels that do not give rise tolabel overlaps and that minimize obscuration of features. Constructionof a good labeling is thus a combinatorial optimization problem, whichhas been shown to be NP-hard (Marks and Shieber, 1991). As ahypothetical baseline algorithm, randomly choosing positions for eachlabel generates a poor labeling, both aesthetically, and as quantifiedusing a metric that counts the number of conflicted labels, i.e., thosethat obscure point features or other labels.

In addition to geographical and technical maps, there are many labelingapplications relating to graph layouts and drawings. These applicationsinclude, but are not limited to, areas such as database design (e.g.entity relationship diagrams), software engineering including CASE,software debugging, complex web pages, CAD drafting, complex electricaldiagrams, and telecommunications and communications networking In fact,the labeling of the graphical features of any drawing is generallynecessary because it conveys information essential to understanding thedrawing. For complex and information rich drawings, computer aidedlabeling is increasingly employed.

As used in the present specification, the term “map” is used to includeboth geographical and technical maps as well as graph layouts anddrawings. The term “label” is used to refer to text or other indicia tobe placed on a map.

A system and method for labeling objects on maps while avoidingcollisions with other labels has been sought after. Some apparentlypowerful algorithms for automatic label placement on maps use heuristicsthat capture considerable cartographic expertise but are hampered byprovably inefficient methods of search and optimization.

This patent discloses a system and method for label placement thatachieves the twin goals of practical efficiency and high labelingquality by employing cartographic heuristics.

SUMMARY OF THE INVENTION

The present invention provides a computer-implemented system and methodof automatically labeling a map in accordance with predefined labellocation, placement, and priority criteria.

Here, each label is represented as a convex polygon with any orientationon the map. Labels have various parameters associated with them such aslocation, size, shape, number and location of vertices, target feature,priority, movement constraints, and clearance. After finding the bestposition of a label for every feature without regard to other labels orfeatures, higher priority label positions are compared to lower prioritylabel positions two at a time. If the labels interfere, the lowerpriority label is moved within its movement constraint. Severalcandidate locations for the lower priority label position are found bymoving it the shortest distance to avoid the higher priority labelposition. A new location is acceptable if the location does not collidewith a label of higher priority. It can collide with a label of lowerpriority. If no candidate positions are acceptable, the label is notmoved. This process continues until all labels are inspected, afterwhich a deviation from the desired result function is calculated. Thisfunction is zero if the label interference for all labels is zero andgreater than zero otherwise. The whole process is repeated until theevaluation function equals zero or the change in the evaluation functionis less than a given percent (e.g., two percent) for a small number(e.g., four) of iterations or if it oscillates for a number (e.g., six)of iterations or if the number of iterations is greater than a setnumber (e.g., twenty). If any interference remains, then interferinglabels with lower priorities are not drawn.

The details of the present invention, both as to its structure andoperation, can best be understood in reference to the accompanyingdrawings, in which like reference to the accompanying drawings, in whichlike reference numerals refer to like parts, and in which:

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram of a computer hardware architecture compatible withthe present system and method.

FIG. 2 is a schematic diagram showing an exemplary computer programproduct.

FIG. 3 is a flow chart showing the overall logic of the present systemand method.

FIGS. 4 a, 4 b, and 4 c is a flow chart showing the initialization ofthe anti-collision system and method.

FIG. 5 is a flow chart of the sorting labels by priority.

FIG. 6 is a flow chart showing the initialization of halting criteriavariables.

FIGS. 7 a and 7 b is a flow chart showing the test of whether each labelhas been tested.

FIG. 8 is a flow chart showing the overlap test FIGS. 9 a, 9 b, and 9 cis a flow chart showing the movement procedure.

FIG. 10 is a flow chart showing the initiation of collision scores andpriority ranges.

FIG. 11 is a flow chart showing the calculation of the evaluationfunction.

FIG. 12 is a flow chart showing the halt routine.

FIG. 13 is a flow chart showing the routine to adjust label properties.

FIG. 14 is a flow chart showing the return to caller.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring initially to FIG. 1, a system is shown which includes adigital processing apparatus. This system is a general-purpose computer1000. The computer may include a graphics display, print hardware, andprint software, or may be as simple as a generic personal computer. Theexample computer in FIG. 1 includes central processor 1010, systemmemory 1015, disk storage 1020 (e.g., hard drive, floppy drive, CD-ROMdrive, and DVD drive), controller 1005, network adapter 1050, videoadapter 1030, and monitor 1055. Data input may be through one or more ofthe following agencies: keyboard 1035, pointing device 1040, diskstorage 1020, local area network 1060, point to point communications1065, and wide area network 1070 (e.g., internet).

One or more features of the computer as shown may be omitted while stillpermitting the practice of the invention. For example, printer 1045 isnot necessary for maps intended to be displayed only on monitor 1055.Likewise, network adapter 1050, local area network 1060, point to pointcommunications 1065, and wide area network 1070 are not necessary whenthe primary method of data input is via removable disk storage.

The flow charts herein illustrate the structure of the logic of thepresent invention as embodied in computer program software. Thoseskilled in the art will appreciate that the flow charts illustrate thestructures of logic elements, such as computer program code elements orelectronic logic circuits, that function according to this invention.Manifestly, the invention is practiced in its essential embodiment by amachine component that renders the logic elements in a form thatinstructs a digital processing apparatus (that is, a computer) toperform a sequence of function steps corresponding to those shown.

FIG. 2 shows a computer program product which includes a disk 1080having a computer usable medium 1085 thereon for storing program modulesa, b, c, and d. While 4 modules are shown in FIG. 2, it is to beunderstood that the number of modules into which the program is dividedis arbitrary and may be in any particular embodiment a different number.

Modules a, b, c, d may be a computer program that is executed byprocessor 1010 within the computer 1000 as a series ofcomputer-executable instructions. In addition to the above-mentioneddisk storage 1020, these instructions may reside, for example in RAM orROM of the computer 1000 or the instructions may be stored on a DASDarray, magnetic tape, electronic read-only memory, or other appropriatedata storage device. In an illustrative embodiment of the invention, thecomputer-executable instructions may be lines of compiled C++ code.

FIG. 3 is an overview and summary of the label anti-collision procedurefor maps. The caller of the procedure performs the first stage, routine5, and the second stage, routine 8. Routine 5 involves locating eachlabel on a map in the optimal position with respect to its targetfeature without regard to other labels or features. Routine 8 assignsproperties to the map and the labels.

To begin, the user must specify how to initially place labels on a map.That is, commencing at routine 5, it is assumed that the user willassign positions that give the best label location with respect to itsassociated feature. For this procedure to work, the user places thelabels in the best spots according to their criteria regardless of otherlabels and map features. For example, in the initial positions, labelsmay overlap each other and/or extend over the map boundary. Labels areassumed to be convex polygons while the map boundary is assumed to be arectangle.

Next, at routine 8, the user must assign properties to the map and thelabels. Map properties include its height and width. A label'sproperties include the associated map feature(s), initial location,size, shape, angular orientation, priority, movement constraints, andclearance. In addition, each label has an associated property thatindicates the fraction of the label area that can extend outside the mapboundary before it is not drawn. The procedure takes all of theseproperties into account to move labels to acceptable positions or to notdraw the label.

The following discussion concerns only those geometric objects in theplane of the map, of which the labels are a part. All labels arerestricted to convex planar polygons in this plane. A planar polygon isconvex if it contains all the line segments connecting any pair of itspoints. If two convex planar polygons overlap, this means that:

-   -   1) at least one vertex of one polygon is inside the other        polygon, or    -   2) at least one edge of one polygon crosses or touches (i.e.,        intersects) an edge of the other polygon.

To begin the anti-collision procedure, three initialization steps occur.First, labels lying partially inside the map boundary must either bemoved completely inside the portrait or be excluded from being comparedto other labels and excluded from being drawn. Each label has movementtypes and constraints that determine whether or not the label qualifiesfor movement completely onto the map. These movement types andconstraints are explained below. Labels qualifying for movement to theinside of the map are moved regardless of the collision status with anyother label.

Second, the labels must be ordered in a list with respect to priorityfrom highest priority to lowest priority. In general, many labels willhave the same priority. Within any group of labels with the samepriority, any particular label is randomly placed within that block.

Third and last, variables that monitor the state of the procedure mustbe initialized.

The purpose of routine 10 is to move labels within the map boundary. Iftoo much of a label is outside the boundary, it will not be included inthe map. Each label is tested to determine what fraction of its area iswithin the map boundary.

At routine 20, labels are sorted in order of descending priority.Halting criteria parameters are initialized at routine 30.

Every combination of two labels is tested for overlap in routine 40.When comparing labels to determine if they overlap, it is important tochoose the order of comparison properly to avoid excessive calculationand moving labels more times than necessary. The highest priority labelsshould be tested for overlap before labels of lower priority.

The overlap test at routine 45 has three parts. First, it must bedetermined if any vertex of a first label is inside the second label.Second, it must be determined if any vertex of a second label is insidethe first label. Third, it must determine if any edge of the first labelintersects any edge of the second label. If at any point either label isdetermined to overlap the other label, then any remaining parts arebypassed.

Labels are moved about the map at routine 50 to clear existing labelcollisions. After it is determined that two labels overlap, the routinefinds several new locations for the lower priority of the two labelsthat eradicate the existing overlap. These locations are ranked by howfar the label must be moved, shortest to longest. Then if appropriate,the lower priority is moved to a new location, and its locationparameters are adjusted.

The evaluation function, routine 60, quantifies the extent of labelcollisions. Routines 40, 45, 50, and 60 iterate until halt routinecriteria 70 are satisfied. Labels may move several times before theiterations stop.

After the iterations stop, all labels are examined for any overlap andlabel properties are adjusted at routine 80. Finally, control isreturned at routine 90 to the user to draw or view the map.

FIGS. 4 a, 4 b, and 4 c display the logic of routine 10 in detail. Thepurpose of routine 10 is to make sure all of a label is within the mapboundary. If too much of a label is outside the boundary, it will not beincluded in the map. Each label is tested to determine what fraction ofits area is within the map boundary. A particular label is divided intoa grid; 32 by 32 cells is a typical division that works well inpractice. If the centroid of a cell is within the map boundary, theentire cell contributes to the fraction of the label within theboundary. The areas of each cell within the map are added to together.If this sum of cell areas, divided by the total label area, is greaterthan a predetermined value, then the label is moved entirely onto themap according to the movement procedure and the movement constraintsdescribed below. The only change to the procedure is that there is notest for overlap with other labels. The qualifying labels are moved ontothe map at this time and tested later.

Step 100 obtains a list of labels from data storage. Each label istested for whether the entire label is inside the map boundary. First,step 108 initializes flags that will be used in routine 10. Step 112tests whether vertices of each label are outside the map boundary. Ifthe vertices of a label are all inside the map boundary, then the nextlabel is tested. If any vertices of a label are outside the mapboundary, then, at step 116, a circumscribing rectangle is placed aroundthe label. Then the circumscribing rectangle is divided into a pluralityof cells at step 120. For example, the rectangle may be divided into 64cells by 64 cells forming a total of 4096 cells.

Each cell is tested, step 124. The test includes finding the centerpoint of each cell to find the number of cells inside the label, step128. Then, at step 132, the center point of each cell used to find thenumber of cells both inside the label and inside the map.

The fraction of the label inside the map boundary is determined at step136. The high and the low values of the x and y coordinates for thevertices of the label are found in step 140. Then the label is tested,step 144, to determine if the fraction of the label inside the mapboundary is high enough to qualify for attempted movement inside themap. There is one of two possible ways the label might move depending onits movement constraints, which is determined in step 148. One movement,in both the x-axis and y-axis direction, is performed in steps 152, 156,160, 164, and 168. In step 152, the x-axis and y-axis movement of thelabel in the plane of the map (2D type movement) is initialized to(0,0). In step 156, the minimum 2D type movement to move the entirelabel within the map is determined (see the following pseudo-code forRoutine 10 which shows how to determine the minimum 2D type movement).

In step 160, the maximum allowed 2D movement parameter for the labelfrom its original position is compared to the minimum 2D type movement.In step 164, it is determined if the label fits within the map boundaryafter the label has been moved by the minimum 2D movement. This isreally a test to see if the label is too big to fit in the map. In step168, if the label can fit in the map, a label flag and a label parameterare set.

The other movement, restricted to a vector, is performed in steps 172,176, 180, 184, and 188. In step 172, the vector type label movementcandidates(s) to move the label within the map is determined (see thefollowing pseudo-code for Routine 10 which shows how to determine theminimum vector movement). In step 176, a loop cycles throughcandidate(s) for the label which are determined in step 172. In step180, if the maximum allowed vector movement parameter for the label fromits original position is less than the magnitude of the currentcandidate for the label, go to step 176. Otherwise, go to step 184. Instep 184, if the label does not fit within the map boundary after thelabel has been moved by the current candidate, go to step 176. This isreally a test to see if the label is too big to fit in the map.Otherwise, go to step 188. In step 188, if the label can fit in the map,a label flag and a label parameter are set. If the label is partially ortotally outside the map, and cannot be properly moved within the map,which is checked in step 192, then a parameter for that label is set instep 196.

Once all labels have been tested, step 104 exits routine 10 and proceedsto routine 20.

Referring to FIG. 5, labels are sorted by priority at step 200 from thehighest priority label to the lowest priority label and placed into adata structure map. Step 210 exits routine 20 and proceeds to routine30, an initialization of halting criteria variables.

In FIG. 6, step 300 initializes halting criteria variables. Step 310exits routine 30 and proceeds to routine 40, a test of every combinationof two labels for overlap.

The above-described logic is further shown in the following pseudo-codewith comments:

PULL IN THE LABELS FROM THE EDGES OF THE MAP ROUTINE //Pseudo-code forthe Initialization of the Anti-collision Procedure for Maps //List ofpseudo-code variables previous_collision_score - the collision scorefrom the previous iteration previous_previous_collision_score - thecollision score from two iterations ago iteration_count - number oftimes the anti-collision procedure has looped slow_change_count - numberof iterations of continuous slow change of collision scoreoscillation_count - number of iterations of continuous oscillation ofcollision score priority_of_most_important_label - numerical priorityvalue of the most important label priority_range - the differencebetween the priority of the least and the most important labels. Thisnumber is non-negative. frac_inside - fraction of label inside the mapboundaries map_x_size - the number of x units in the map - map boundaryis a rectangle map_y_size - the number of y units in the map - mapboundary is a rectangle  (xMove2D, yMove2D) - the label movement if thelabel qualifies for movement completely inside the map boundary and thelabel parameters specify 2D type movement  (xMoveVec[ ], yMoveVec[ ]) -an array of label movements if the label qualifies for movementcompletely inside the map boundary and the label parameters specifyvector type movement  (xc, yc) - center point of a cell formed from agrid within the circumscribing rectangle around the label  (x_IP,y_IP) - a point satisfying various conditions used to properly move alabel completely inside the map boundaryLABEL_TOO_MUCH_OUTSIDE_PORTRAIT - indicates if the procedure hasdetermined that the label has much area outside the map boundary or cannot be properly moved to a new position completely inside the mapboundary. This is a flag of every label set by the procedure.LABEL_OUTSIDE_PORTRAIT - Not used. This is a flag of every label set bythe procedure. LABEL_MOVED_INTO_PORTRAIT - indicates if the procedurehas moved a label that was originally partially outside the map boundaryto a new position completely inside the map boundary. This is a flag ofevery label set by the procedure. LABEL_MIN_FRACTION_INSIDE - minimumfraction of the label that must be inside the map boundary to attemptrelocation completely inside the map boundary. This is a parameter ofevery label set by caller. LABEL_NEW_LOCATION - A vector (x, y) which isadded to all vertices of a label if the procedure moves the label. Thisvector has an initial value of (0, 0). This is a parameter of everylabel determined by the procedure. // pseudo-code also has: // a list ofpossible label movement candidates to pull the label inside the mapboundary // a data structure map of labels and their properties sortedby priority from the most // important label to the least importantlabel ------------------------------------------------------------ //THIS IS THE START OF ROUTINE 10 // The labels are not in any particularorder at this point. // They are only in the order in which they arereceived from the caller. for i = first unordered label to lastunordered label  set label i flag LABEL_OUTSIDE_PORTRAIT = FALSE  setlabel i flag LABEL_TOO_MUCH_OUTSIDE_PORTRAIT =  FALSE  set label i flagLABEL_MOVED_INTO_PORTRAIT = FALSE  set label i parameterLABEL_NEW_LOCATION = (0, 0)  // Determine if the label is inside oroutside the map boundary.  // If all vertices are inside, then theentire label is inside.  // Here, a vertex on the map boundary is insidethe boundary.  label_inside_map = TRUE  for j = first vertex of label ito last vertex of label i  if ( vertex j outside map boundary ) {  label_inside_map = FALSE  }  next j  if ( label_inside_map = FALSE ) { // Below, find the approximate fraction of the label inside the mapboundary.  // The circumscribing rectangle has edges parallel to the mapedges.  // Note that both the rectangle and the label are convexpolygons.  Put a circumscribing rectangle around label i  Divide thecircumscribing rectangle into 64 units by 64 units forming 4096 cells in_label = 0  in_label_and_map = 0  for k = first cell to last cell  Find center point of cell k called (xc, yc)   // Here, a point on alabel edge or map boundary is inside the label or map.   // Use the“point inside convex polygon” procedure described in the   // labelsoverlap section.   if( (xc, yc) inside label ) {   in_label = in_label +1   if( (xc, yc) inside map boundary ) {    in_label_and_map =in_label_and_map + 1   }   }  next k  frac_inside = ( in_label_and_map)/( in_label )  // Move the label inside the map boundary if enough ofthe label is inside.  // Some of the vertices below may be the samevertex.  (x_low, yL) = coordinates of vertex with lowest x coordinate (x_high, yH) = coordinates of vertex with highest x coordinate  (xL,y_low) = coordinates of vertex with lowest y coordinate  (xH, y_high) =coordinates of vertex with highest y coordinate  // find the newlocation for the label  if ( frac_inside > LABEL_MIN_FRACTION_INSIDE parameter of label i ) {   if ( 2D type movement for label i ) {  (xMove2D, yMove2D) = (0, 0)   // If both conditions are true, thelabel will not fit into the map.   if ( x_low < 0 ) {    xMove2D = 0 −x_low   }   else if ( x_high > map_x_size − 1 ) {    xMove2D =map_x_size − 1 − x_high   }   // If both conditions are true, the labelwill not fit into the map.   if ( y_low < 0 ) {    yMove2D = 0 − y_low  }   else if ( y_high > map_y_size − 1 ) {    yMove2D = map_y_size − 1− y_high   }   // Determine if the label is still within its movementparameters.   // This means has the label moved too far from itsoriginal position.   // The original location parameter is neverchanged. It does not change   // because it is always used forcomparison to the new position.   if ( (xMove2D, yMove2D) within label i2D type movement   parameters ) {    // Determine if the label is stillinside the map boundary after movement.    // This is really a test tosee if the label is too big to fit in the map.    // Here, a vertex onthe map boundary is not outside the map.    // This test works becauseboth label and map are convex    polygons.    for j = first vertex oflabel i to last vertex of label i    label_moved_outside_map = FALSE   if ( ( vertex j + (xMove2D, yMove2D) ) of label i is outside mapboundary ) {     label_moved_outside_map = TRUE    }    next j    if (label_moved_outside_map = FALSE ) {    set label i flagLABEL_MOVED_INTO_PORTRAIT =    TRUE    set label i parameterLABEL_NEW_LOCATION =    (xMove2D, yMove2D)    }   }   }   else { //vector type movement   count = 0   // If both conditions are true, thelabel will not fit into the map.   if ( x_low < 0 ) {    find a point(x_IP, y_IP) which meets the following   requirements contained by aline parallel to the vector type   movement contained by a the line x =0   contained by a line also containing (x_low, yL)  if ( (x_IP, y_IP)exists ) {   xMoveVec[count] = x_IP − x_low   yMoveVec[count] = y_IP −yL   place in list of possible label movement candidates   count =count + 1  }  }  else if ( x_high > map_x_size − 1 ) {  find a point(x_IP, y_IP) which meets the following requirements   contained by aline parallel to the vector type movement   contained by a the line x =map_x_size − 1   contained by a line also containing (x_high, yH)  if ((x_IP, y_IP) exists ) {   xMoveVec[count] = x_IP − x_high  yMoveVec[count] = y_IP − yH   place in list of possible label movementcandidates   count = count + 1  }  } // If both conditions are true, thelabel will not fit into the map.  if ( y_low < 0 ) {  find a point(x_IP, y_IP) which meets the following requirements   contained by aline parallel to the vector type movement   contained by a the line y =0   contained by a line also containing (XL, y_low)  if ( (x_IP, y_IP)exists ) {    xMoveVec[count] = x_IP − xL    yMoveVec[count] = y_IP −y_low    place in list of possible label movement candidates    count =count + 1   }   }   else if ( y_high > map_y_size − 1 ) {   find a point(x_IP, y_IP) which meets the following requirements    contained by aline parallel to the vector type movement    contained by a the line y =map_y_size − 1    contained by a line also containing (xH, y_high)   if( (x_IP, y_IP) exists ) {    xMoveVec[count] = x_IP − xH   yMoveVec[count] = y_IP − y_high    place in list of possible labelmovement candidates    count = count + 1   }   }   // Can have zero,one, or two possible label movement candidates   for k = 0 to (count− 1)   // Determine if the label is still within its movementparameters.   // This means has the label moved too far from itsoriginal position.   // The original location parameter is neverchanged. It does not change   // because it is always used forcomparison to the new position.   move_distance = magnitude of(xMoveVec[k], yMoveVec[k])   if ( move_distance within label i  vectortype movement parameters ) {    // Determine if the label is stillinside the map boundary after movement.    // This is really a test tosee if the label is too big to fit in the map.    // Here, a vertex onthe map boundary is not outside the map.    // This test works becauseboth label and map are convex polygons.    for j = first vertex of labeli to last vertex of label i     label_moved_outside_map = FALSE     if((vertex j + (xMoveVec[k], yMoveVec[k])) of label i is outside mapboundary) {     label_moved_outside_map = TRUE     }    next j    if (label_moved_outside_map = FALSE ) {     set label i flagLABEL_MOVED_INTO_PORTRAIT =     TRUE     set label i parameterLABEL_NEW_LOCATION = (xMoveVec[k], yMoveVec[k])     break out of loop //go past next k    }    }   next k   } // end of vector type movement  } if ( label i flag LABEL_MOVED_INTO_PORTRAIT = FALSE ) {   set label iflag LABEL_TOO_MUCH_OUTSIDE_PORTRAIT =   TRUE  }  } // end iflabel_inside_map = FALSE next i // THIS IS THE START OF ROUTINE 20 //Sort the labels by priority. // The labels with the highest prioritieshave the lowest numbers. // Priorities may be negative numbers. //Labels may have the same priority. // After this loop, assume all labelsare ordered properly. Sort labels by priority from the most importantlabel to the least important label  and place into a data structure map// THIS IS THE START OF ROUTINE 30 // Initialize halting criteriavariables priority_range = priority_of_least_important_label −priority_of_most_important_label // initialize these two variables tolarge numbers previous_collision_score = Very Large Numberprevious_previous_collision_score = Very Large Number iteration_count =0 slow_change_count = 0 oscillation_count = 0

Referring to FIGS. 7 a and 7 b, labels are compared to determine if theyoverlap (routine 40). The number of labels and the maximum numericaldifference between the highest and lowest priority labels is determinedin step 400. All labels are grouped according to priority.

In step 403, a loop cycles through all the priorities from the highestpriority (i.e. priority 0) to the lowest priority of the labels (i.e.priority last_Pri), for every integer from 0 to last_Pri. In step 406,it is determined if there are any labels corresponding to the currentpriority in the loop. If there are no labels with the current priorityof the loop, then in step 409, set the value of array first_label[current priority of loop] to −1 and set the value of the array lastlabel [current priority of loop] to −1. If there are labels with thecurrent priority of the loop, then in step 412, set the value of arrayfirst_label [current priority of loop] to the index of the mostimportant label with priority p and set the value of the arraylast_label [current priority of loop] to the index of the leastimportant label with priority p.

It is important to choose the order of comparison properly to avoidexcessive calculation and moving labels more times than necessary. Thispart compares two labels using loops. In step 415, the loop for thefirst label starts at priority 0 and goes to priority last_Pri. In step421, if the value of the variable:

first_label [current priority of first loop]

is equal to −1, then go back to the beginning of loop for the firstlabel. Otherwise, go to step 424.

In step 424, the loop for the second label starts at the currentpriority of the first loop and goes to priority ‘last_Pri.’ In step 427,if the value of the variable:

first_label [current priority of second loop]

is equal to −1, then go back to the beginning of loop for the secondlabel. Otherwise, go to step 430.

In step 430, a third loop starts at the index in the list of labels ofthe first label with a priority equal to the current priority of thefirst loop and goes to the index in the list of labels of the last labelwith a priority equal to the current priority of the first loop. In step433, if the label with the current index in the list of labels from theloop in step 430 is completely outside of the map or too much of thelabel is outside of the map, then go back to step 430. Otherwise, go tostep 436.

In step 436, a fourth loop starts at the index in the list of labels ofthe first label with a priority equal to the current priority of thesecond loop and goes to the index in the list of labels of the lastlabel with a priority equal to the current priority of the second loop.When step 436 has finished examining the relevant labels, then step 436returns to step 430. As discussed above, when step 430 has finishedexamining the relevant labels, then step 430 returns to step 424. Ifstep 426 has not finished examining the relevant labels, then proceed tostep 439. In step 439, if the label with the current index in the listof labels from the loop in step 436 is completely outside of the map ortoo much of the label is outside of the map, then go back to step 436.Otherwise, go to step 442. In step 442, if the current label index ofthe loop in step 430 is less than or equal to the current label index ofthe loop in step 436, then go to step 436. Otherwise, go to step 445.

Step 445, which corresponds to routine 45, tests for overlap between themembers of the pair. Step 448, which corresponds to routine 50, performsthe movement procedure on one of the labels if they overlap. Step 418exits routine 40 and proceeds to routine 60, an evaluation functionprocedure.

The above-described logic is further shown in the following pseudo-codewith comments:

Order of Comparison for the Label Overlap Test Routine // The n labelshave already been sorted in priority order, // from the most important,label 0, consecutively, // to the least important, label (n − 1).LABEL_TOO_MUCH_OUTSIDE_PORTRAIT - indicates if the procedure hasdetermined that the label has much area outside the map boundary or cannot be properly moved to a new position completely inside the mapboundary. This is a flag of every label set by the procedure.LABEL_OUTSIDE_PORTRAIT - Not used. This is a flag of every label set bythe procedure. LABEL_MOVED_INTO_PORTRAIT - indicates if the procedurehas moved a label that was originally partially outside the map boundaryto a new position completely inside the map boundary. This is a flag ofevery label set by the procedure. last_Label_Index = number_of_labels −1;  // zero based // Zero based. // The highest priority is zero and thelowest priority is a number greater than zero. // Note that there may bepriorities which have no labels. last_Pri = lowest priority − highestpriority;  // which equal the lowest priority // Below, if there are nolabels with priority p, // first_Pri[p] = −1 and last_Pri[p] = −1 //first_label[p] = first label index with priority p // last_label[p] =last label index with priority p for p = 0 to last_Pri;  // highestpriority to lowest priority  if labels with priority p exist first_label[p] = most important label with priority p;  last_label[p] =least important label with priority p;  else  first_label[p] = −1; last_label[p] = −1; next p; for i_pri = 0 to last_Pri;  // highestpriority to lowest priority  if first_label[i_pri] = −1, continue tonext i_pri;  for j_pri = i_pri to last_Pri;  // highest priority tolowest priority  if first_label[j_pri] = −1, continue to next j_pri; for i_idx = first_label[i_pri] to last_label[i_pri];  if i_idx flagLABEL_TOO_MUCH_OUTSIDE_PORTRAIT =       TRUE OR LABEL_OUTSIDE_PORTRAIT =TRUE,       continue to next i_idx   for j_idx = first_label[j_pri] tolast_label[j_pri];   // Do not compare a label to itself or   // comparelabels which have been previously compared,   // for this particulariteration of the entire algorithm.   if i_idx <= j_idx, continue to nextj_idx;   if j_idx flag LABEL_TOO_MUCH_OUTSIDE_PORTRAIT =        TRUE ORLABEL_OUTSIDE_PORTRAIT = TRUE,        continue to next j_idx   if labeli_idx overlaps label j_idx,     then perform the label movementprocedure on label j_idx;   next j_idx;  next i_idx;  next j_pri; nexti_pri;

All labels are restricted to convex planar polygons in the plane of themap. A planar polygon is convex if it contains all the line segmentsconnecting any pair of its points. If two convex planar polygonsoverlap, this means that:

1) at least one vertex of one polygon is inside the other polygon, or

2) at least one edge of one polygon intersects an edge of the otherpolygon.

Routine 45, shown in FIG. 8, is a label overlap test procedure. Theoverlap test has three parts. First, it determines if any vertex of thefirst polygon is inside the second polygon, step 462. Second, itdetermines if any vertex of the second polygon is inside the firstpolygon, step 466. Third, it determines if any edge of the first polygonintersects any edge of the second polygon, step 470. Once any vertex isfound to be inside the other polygon, there is no need to test remainingvertices and edges. Once any edge is found to intersect any edge of theother polygon, there is no need to test remaining edges and vertices.

Prior to the overlap test, routine 45 begins by receiving two labelsfrom caller in step 450. In step 454, the maximum and minimum x and yvalues for each label are determined. These x and y values formcircumscribing rectangles, whose edges are parallel to the map's x axisand y axis, for each label. In step 458, the circumscribing rectanglesfor each label are compared. If these circumscribing rectangles do notoverlap, then routine 45 returns “no overlap” to the caller in step 478.

FIG. 8 shows the test for whether a vertex of a polygon is insideanother polygon. The method is shown in “Determining if a Point Lies onthe Interior of a Polygon,” Paul Bourke (available on the world wideweb). Consider the standard right-handed two-dimensional Cartesiancoordinate system with the positive y direction up and the positive xdirection to the right. A first polygon's edges are chosen such that theperimeter is traversed in the counterclockwise (CCW) direction (theperimeter may be traversed in a clockwise direction so long as it isdone consistently). At step 462, if any vertex of a second polygon is tothe left of all edges of the first polygon, then that vertex is insidethe first polygon. Likewise, at step 466, if any vertex of the firstpolygon is to the left of all edges of the second polygon then thatvertex is inside the second polygon. If any vertex of a polygon isinside another polygon, then the polygons overlap. This is the test fora point being inside a convex planar polygon.

Lines containing the edges that make up a polygon may be written,(y−Y1)(X2−X1)−(x−X1)(Y2−Y1)=0where(x,y) is any point on the line, and(X1,Y1) and (X2,Y2) are the endpoints of an edge of the polygon undertest.Points lying on the polygon edges satisfy the line equations, whilepoints not on the polygon edges do not satisfy those equations. If (x,y) is any point in the plane, the equation for a line containing an edgeis:(y−Y1)(X2−X1)−(x−X1)(Y2−Y1)=Kwhere K is a real number constant.

Then, for all points to the left of any edge, K>0, and for all points tothe right of any edge, K<0. Note that point 2 in the above equation isat the head of the vector representing the edge and point 1 is at thetail of the vector representing edge. This is true because, for alledges pointing to the right, (X2−X1)>0. For any point above the linecontaining the edge, (x_above, y_above), there exists a point, (x,y), onthe line, such that:

  x_above = x  and  y_above > y   Therefore:(y − Y 1)(X 2 − X 1) − (x − X 1)(Y 2 − Y 1) = (y − Y 1)(X 2 − X 1) − (x − X 1)(Y 2 − Y 1)(y_above − Y 1)(X 2 − X 1) − (x − X 1)(Y 2 − Y 1) > (y − Y 1)(X 2 − X 1) − (x − X 1)(Y 2 − Y 1)(y_above − Y 1)(X 2 − X 1) − (x_above − X 1)(Y 2 − Y 1) > (y − Y 1)(X 2 − X 1) − (x − X 1)(Y 2 − Y 1)

A point that is above a line pointing to the right is a point that liesto the left of the line. Similar arguments show that any point on theleft of lines pointing up, pointing down, or pointing left yields apositive value with substituted into the line equation.

Step 470 tests whether the edges of one polygon intersect anotherpolygon. Consider the equations of the lines that contain the edges ofthe first polygon and the equations of the lines that contain the edgesof the second polygon. Determine the intersection point for everytwo-line combination, where one line is a line that contains an edge ofthe first polygon and the other line is a line that contains an edge ofthe second polygon. If the intersection point lies on or between theendpoints of the polygon edges, then the edge of one polygon intersectsthe edge of the other polygon and the polygons overlap. In cases wherethe lines are parallel, and not coincident, no intersection point existsfor that pair of lines. If the lines are coincident, then the edges mayor may not touch, but if the edges touch then the polygons overlap.

If the three above overlap tests, at step 462, step 466, step 470, findan overlap between the two labels, then routine 45 returns “labelsoverlap” to the caller in step 482, step 486, and step 490,respectively. If after performing the three tests, there is no overlapbetween the two labels, then routine 45 returns “no overlap” to thecaller in step 474.

The above-described logic is further shown in the following pseudo-codewith comments:

Pseudo-code for the Overlap Test of Convex Planar Polygons List ofpseudo-code variables  (x_2_i, y_2_i) - vertex i of polygon 2  (X1_j,Y1_j) - vertex 1 of edge j of polygon 1  (X2_j, Y2_j) - vertex 2 of edgej of polygon 1  (x_IP, y_IP) - intersection point of lines containingedges x_max_i - max x of edge i y_min_j - min y on edge j find max x,max y, min x, min y on polygon 1 - each will be on a vertex find max x,max y, min x, min y on polygon 2 - each will be on a vertex // if anyexpression is true, the polygons do not overlap, so return false if (minx of polygon 1 >= max x of polygon 2) RETURN NO_OVERLAP if (min x ofpolygon 2 >= max x of polygon 1) RETURN NO_OVERLAP if (min y of polygon1 >= max y of polygon 2) RETURN NO_OVERLAP if (min y of polygon 2 >= maxy of polygon 1) RETURN NO_OVERLAP // if any vertex of polygon 2 isinside polygon 1, the result is greater than zero. // proceed aroundpolygon 1 in the CCW direction for each vertex of polygon 2 for i =first vertex of polygon 2 to last vertex of polygon 2  inside = TRUE for j = first edge of polygon 1 to last edge of polygon 1 in CCWdirection  if((y_2_i − Y1_j) (X2_j − X1_j) − (x_2_i − X1_j)  (Y2_j −Y1_j) <= 0) inside = FALSE  next j  if (inside = TRUE), RETURN OVERLAPnext i Repeat the above, except test polygon 1 vertices with polygon 2edges Return OVERLAP if appropriate // perform the edge intersectiontest for i = first edge of polygon 1 to last edge of polygon 1  of thetwo endpoints of edge i, get x_max_i, y_max_i, x_min_i,  y_min_i  for j= first edge of polygon 2 to last edge of polygon 2  of the twoendpoints of edge j, get x_max_j, y_max_j, x_min_j, y_min_j  solve forintersection point, (x_IP, y_IP), of lines containing edge i and edge j if intersection point exists   // An intersection at an endpoint is anoverlap.   // These tests also take care vertical and horizontal edges.  if (x_IP <= x_max_i and x_IP >= x_min_i) and   (y_IP <= y_max_i andy_IP >= y_min_i) and   (x_IP <= x_max_j and x_IP >= x_min_j) and   (y_IP<= y_max_j and y_IP >= y_min_j), RETURN OVERLAP  next j next i RETURNNO_OVERLAP

Labels must be moved about the map to clear existing label collisions.After it is determined that two labels overlap, routine 50 (FIGS. 9 a, 9b, and 9 c) finds several new locations for the lower priority of thetwo labels that eradicate the existing overlap. The higher prioritylabel is a first label while a lower priority label is a second label.These locations are ranked by how far the second label must be moved,shortest to longest. The actual location finally selected must meet thefollowing criteria:

-   -   1) the second label moves a shorter distance than other        qualifying locations;    -   2) the second label movement does not result in overlap with        another label (or labels) of equal or higher priority than the        first label;    -   3) the second label movement does not exceed the maximum        movement parameters for that particular label; and    -   4) no part of the second label is moved outside the map        boundary.

If no candidate locations meet these criteria, the second label is notmoved. During the process of fixing existing collisions, othercollisions may be created. New collisions are only allowed if it reducescollisions among labels with priorities equal to or higher than thefirst label. As the procedure iterates, new collisions are handled likethe original collisions. The procedure will minimize collisions.

Each label may be moved in one of two ways. A caller selects the type ofmovement of a label to the exclusion of the other type of movement.First, a label may move in any direction on the map, up to a maximumdistance from the original location. This is referred to as 2D typemovement. Second, a label may move parallel to a vector up to a maximumdistance from the original location in the positive vector direction orthe negative vector direction. This is referred to as vector typemovement that may be used for linear features such as highways andrivers. Both the vector and the maximum distances are in the label'sparameter list. Labels on a map may consist of any mixture of 2Dmovement and vector movement types. However, higher priority labels mustbe examined before lower priority labels regardless of movement type.

Prior to the attempted label movement, routine 50 begins by receivingtwo labels from caller in step 500. Routine 50 cycles through the edgesof first label in step 503 and cycles through the vertices of secondlabel in step 509. A counter is set in step 506. The first label's edgesare traversed in a CCW direction. Remembering that these operations takeplace on a two dimensional map, step 512 tests whether each vertex ofthe second label is left of a line containing an edge of the first labelwhen the first label is traversed in a CCW direction. A vertex of thesecond label is said to be on a label side of the line containing theedge of the first label if the vertex of the second label and area ofthe first label are on the same side of the line containing the edge ofthe first label. Note that these labels are restricted to convexpolygons so all of one label will be on one side of the line containingthe label's edge and no part of the label will be on the other side ofthe line. Likewise, a vertex of a second convex polygon is said to be ona convex polygon side of a line containing an edge of a first convexpolygon if the vertex of the second convex polygon and area of the firstconvex polygon are on the same side of the line containing the edge ofthe first convex polygon. If step 515 specifies a 2D type movement, thenstep 518 finds an intersection of two lines. A first line is the linethat contains one edge of the first label. A second line isperpendicular the first line and contains the vertex. If, instead, step515 specifies a vector type movement, then step 521 finds anintersection of a line containing an edge and a line parallel to thevector type movement also containing the vertex.

If in either the 2D type movement case or the vector type movement case,an intersection exists, step 524, and the vertex is on the label side asdefined above, step 527 calculates a first vector from the vertex to theintersection. If the first vector is too small, step 530, then theroutine 50 calculates, in steps 533, 536, and 539, a second vector withdesirable properties listed in steps 536 and 539. In the case that thefirst vector is too small, the first vector is replaced by the secondvector. Whichever vector remains, it is hereafter referred to as thevector.

Step 542 tests whether the vector is within movement bounds from theoriginal label location. If at step 545, it is within bounds, the vectoris placed on an end of a list of qualified vectors and a length of thevector is placed on an end of a length list. Once all vertices of thesecond label are tested, if there any qualified vectors (step 548),then, at step 551:

-   -   1) Find the maximum length in the length list and a        corresponding qualified vector from the vector list;    -   2) Insert the length and the qualified vector into a data        structure map that is sorted by distance; and    -   3) Empty the length list and vector list.

After all the edges of the first label are checked, at step 554 thesteps starting at step 512 are repeated using the edges of the secondlabel and the vertices of the first label. For any qualifying vectors, anegative of the vector is taken and that vector and its length areinserted into the data structure map.

Next, tests are performed to determine if proposed locations for thesecond label are acceptable. At step 560, starting with a shortestvector in the data structure map, the second label is moved in both adirection and a length of the shortest vector to obtain a new locationfor the second label. Then, at step 563, a test is performed todetermine if part of the new location for the second label is outsidethe map boundary. If, the new location for the second label places partof the second label outside the map boundary, repeat steps 557, 560, and563, using a next vector from the data structure map. Step 566 retrieveslabels with priorities greater than or equal to the first label. In step569, if any retrieved label is the first label or the second label, thenretrieve the next label in step 566. At step 572, the overlap test isperformed on the current candidate location for the second label againstlabels that fail tests at step 563 and step 569. If there is an overlap,steps 557 through 572 are repeated. Otherwise, the second label is movedto the candidate location in step 575. After a new location is found forthe second label among the proposed locations, or after all proposedlocations are determined to be unacceptable, then data structure map iscleared in step 578, and a next pair of labels is supplied in step 581.

The above-described logic is further shown in the following pseudo-codewith comments:

Movement Procedure of Convex Planar Polygons // List of pseudo-codevariables  (x_2_j, y_2_j) - vertex j of polygon 2  (X1_i, Y1_i) - vertex1 of edge i of polygon 1  (X2_i, Y2_i) - vertex 2 of edge i of polygon 1 (x_IP, y_IP) - intersection point of lines containing edge and vertex (X,Y) - vector from vertex to edge pseudo-code also has:  a list ofdistances  a list of vectors  a data structure map of distances andvectors sorted by distance, short to long // Polygon 1 is the moreimportant polygon and polygon 2 will move if possible // Here, thevertices in a polygon are on the left side of the edge // of the otherpolygon when traversing it in the CCW direction, // but the vertices arenot necessarily inside the other polygon. // That is why allpossibilities are caught in the algorithm below - // even where novertex from either polygon is inside the other. // Do not have to checkspecifically for the above case. // If a vertex of polygon 2 is on leftside a polygon 1 edge, the result is greater than zero. // proceedaround polygon 1 in the CCW direction for each vertex of polygon 2 //Note the the vertex in question does not have to be inside polygon 1 fori = first edge of polygon 1 to last edge of polygon 1 in CCW direction count_of_possible_vertices = 0  for j = first vertex of polygon 2 tolast vertex of polygon 2  if((y_2_j − Y1_i)(X2_i − X1_i) −  (x_2_j −X1_i)(Y2_i − Y1_i) > 0)  if (2D type movement for polygon 2)   // asolution will always exist for this case   solve for intersection point,(x_IP, y_IP), of a line containing edge i   and a line perpendicular toedge i containing (x_2_j, y_2_j)   if (vector type movement for polygon2)   // a solution might not exist for this case   solve forintersection point, (x_IP, y_IP), of a line containing edge i   and aline parallel to the vector type movement containing (x_2_j, y_2_j)   if( solution exits for (x_IP, y_IP) )   // get vector from vertex tointersection point    (X,Y) = (x_IP − x_2_j, y_IP − y_2_j)   if ( (X,Y)length minute )    if ( 2D type movement for polygon 2 )    find a point(X,Y) which meets the following requirements     on right side of edge i(CCW)     contained by a line perpendicular to edge i     contained by aline also containing (x_IP, y_IP)     a minute distance from (x_IP,y_IP)    else // vector type movement for polygon 2    find a point(X,Y) which meets the following requirements     on right side of edge i(CCW)     contained by a line parallel to the vector type movement    contained by a line also containing (x_IP, y_IP)     a minutedistance from (x_IP, y_IP)   // because polygon may move several times,keep the original location of the label   if ( movement of (X,Y) leavespolygon with movement limit )    // Make vector just a bit larger thatthe distance to the edge    // so when polygon 2 is moved, it moves justoutside the polygon 1    length_of_XY = length of (X, Y) * (1.0 +1.0e−09)    X = X * (1.0 + 10e−09)    Y = Y * (1.0 + 10e−09)    appendlength_of_XY to end of distance list    append (X,Y) to end of vectorlist    count_of_possible_vertices = count_of_possible_vertices + 1 next j  if (count_of_possible_vertices > 0)  find the maximum distancein the distance list  get the corresponding vector to this distance fromthe vector list  insert the distance and the vector into the datastructure map sorted by distance,  from the shortest distance to thelongest distance  empty distance list and vector list next i Repeat theabove, except use polygon 1 vertices and with polygon 2 edges The vectorfor possible movement, (X,Y), is reversed Insert the results into thesame distance/vector data structure map // the outer loop is just goingthought the sorted data structure map for i = first location candidateto last location candidate  get new location for polygon by addingvector (X,Y) to each vertex  if ( any part of label outside map boundary) next i  for j = first label to last label whose priority >= polygon 1  if ( polygon 1 is label j or polygon 2 is label j) next j   if (polygon 2 in location candidate i overlaps label j ) next i   updatepolygon 2 location in its parameter list   break out of both for loops next j next i clear the data structure map get the next pair of labelsto be tested for overlapThe Evaluation Function, the Halting Criteria, and the Adjustment ofLabel Properties

The following pseudo-code contains a reminder to initialize collisionscores and priority ranges at the top of the procedure. This is shown inFIG. 10, assignment 590.

It is probable that the process of label movement will iterateindefinitely, therefore halting criteria are needed. An evaluationfunction provides input to a halting procedure to stop the process at anacceptable point. The calculation of the evaluation function isrepresented by routine 60 as shown in FIG. 11. All labels that overlapare known at this point. The procedure used to reduce label collisionsis an iterative process. A collision score is a variable that measuresthe severity of collisions of labels in the map. It is initialized tozero in step 600. Step 605 performs cycling through label pairs. In step610, each label of the current pair of labels is tested to see if it hastoo much of its area outside the map or if it is completely outside themap. This avoids unnecessary calculation for labels that will not beused. The overlap test (routine 45) is performed in step 615. If nooverlap occurs between the two labels being tested, then another uniquepair of labels is fetched in step 605. If overlap occurs, then thecollision score is added to the previous collision score in step 620.The final value of the collision score is attained after all the uniquelabel pairs have been tested. In this anti-collision procedure for maps,the evaluation function at step 620 is:

${{Collision}\mspace{14mu}{Score}} = {\sum\limits_{ij}\left( {\left( {{label}\mspace{14mu} i\mspace{14mu}{adjusted}\mspace{14mu}{priority}} \right)^{2} + \left( {{label}\mspace{14mu} j\mspace{14mu}{adjusted}\mspace{14mu}{priority}} \right)^{2}} \right)}$where the score is the summation over every pair of overlapping labels.The result of this function is defined as zero if no collisions remainand greater than zero if any collisions remain. The function penalizesdisproportionately for collisions involving high priority labels. Forinstance, a collision involving a high priority label and a low prioritylabel gets a higher score (worse) than a collision involving two mediumpriority labels.

Routine 70 as shown in FIG. 12 evaluates halting criteria to determineif the labels are in optimal locations. The iterative process must haltat some point. A slow change halting criteria is evaluated in step 700.If the slow change per iteration in the collision score occurs, the slowchange count is incremented by one in step 705. If the slow change periteration does not occur, the slow change variable is reset to zero instep 710. A short-term oscillation halting criteria is evaluated in step715. If the short-term oscillation in the collision score occurs, theshort-term oscillation count is incremented by one in step 720. If theshort-term oscillation does not occur, the short-term oscillation countis reset to zero in step 725. The previous values of the collision scoreare stored in step 730. Step 730 also increments the iteration count byone. Here, an iteration is one cycle of the anti-collision algorithmthat includes routines 40, 45, 50, and 60. Example rules tested at step735 to halt the procedure follow:

-   -   1) the evaluation function is below a minimum value;    -   2) the number of iterations is greater than a maximum value;    -   3) the evaluation function changes less than a minimum        percentage of the previous iteration for more than a set number        of iterations; and    -   4) the evaluation function oscillates for more than a set number        of consecutive iterations.

If none of these conditions is met, the anti-collision algorithm isrepeated in step 740, noting that labels may move several times beforethe iterations stop. A label's new position is stored in its parameterlist at the time a label is moved. The original position is alwaysavailable in the label's parameter list.

Routine 80, as shown in FIG. 13, adjusts label properties. At thispoint, labels will not be moved because the halting criteria have beensatisfied. However, some labels may still overlap. Routine 80 begins instep 800 by setting the DRAW flag to TRUE for every label. Step 805performs cycling through label pairs. In step 810, each label of thecurrent pair is tested to see if it has too much of its area outside themap or if it is completely outside the map. This avoids unnecessarycalculation for labels that are not used. Labels that have some or allof their area outside the map have their DRAW flag set to FALSE in step815. The overlap test (routine 45) is performed in step 820 on thoselabel pairs for which neither have any area outside the map. If nooverlap occurs between the two labels being tested, then another uniquepair of labels is fetched in step 805.

Otherwise, go to step 825. In step 825, if both labels have MUSTDRAW=TRUE, then go to step 840. Otherwise, go to step 830. In step 830,if the first label has MUST DRAW=TRUE, then go to step 840. Otherwise,go to step 835. In step 835, if the second label has MUST DRAW=TRUE,then go to step 845. Otherwise, go to step 840. In step 840, the secondlabel has its draw flag set to DRAW=FALSE. In step 845, the first labelhas its draw flag set to DRAW=FALSE. Here, the first label is higher onthe list of labels than the second label.

These flags are in the label's parameter list. The MUST DRAW flag is setby the caller. If the DRAW flag is true, this procedure will draw thelabel. If the DRAW is false, this procedure will not draw the label. Forany pair of overlapping labels, the following somewhat arbitrary rulesdetermine the final state of a label's DRAW flag:

-   -   1) If one label has MUST DRAW=TRUE, that label sets DRAW=TRUE,        and the second label sets DRAW=FALSE.    -   3) If both labels have MUST DRAW=TRUE, the label higher on the        list of label priority sets DRAW=TRUE, and the other label sets        DRAW=FALSE. Note that this will hold for labels of equal        priority.    -   4) If neither label has MUST DRAW=TRUE, the label higher on the        list of label priority sets DRAW=TRUE, and the other label sets        DRAW=FALSE. Note that this will hold for labels of equal        priority.

The label priority list and the overlap test are described in precedingsections of the description of the entire anti-collision procedure.

After label properties are adjusted, control is returned to the caller,in step 900 of FIG. 14.

The above-described logic is further shown in the following pseudo-codewith comments.

Pseudo-Code for the Evaluation Function, the Halting Criteria, and theAdjustment of Label Properties

List of pseudo-code variables collision_score - the sum of theevaluation function after each Iteration previous_collision_score - thecollision score from the previous iterationprevious_previous_collision_score - the collision score from twoiterations ago iteration_count - number of times the anti-collisionprocedure has Looped slow_change_count - number of iterations ofcontinuous slow change of collision score oscillation_count - number ofiterations of continuous oscillation of collision scorepriority_of_most_important_label - numerical priority value of the mostimportant label priority_range - the difference between the priority ofthe least and the most important labels. This number is non-negative.adjusted_priority_1 - the label 1 priority modified to make it work inthe evaluation function // Initialize halting criteria variablespriority_range = priority_of_least_important_label -priority_of_most_important_label // initialize these two variables tolarge numbers previous_previous_collision_score = Very Large Numberiteration_count = 0 slow_change_count = 0 oscillation_count = 0 //------ The above must be done at the top of the procedure -------- // //Evaluation Function -----------------------------------------------collision_score = 0 // these loops go thought label priority list for i= first label to last label  if( label i flagLABEL_TOO_MUCH_OUTSIDE_PORTRAIT = TRUE OR    label i flagLABEL_OUTSIDE_PORTRAIT = TRUE ) next i  for j = label i+1 to last label if( label j flag LABEL_TOO_MUCH_OUTSIDE_PORTRAIT = TRUE OR    label jflag LABEL_OUTSIDE_PORTRAIT = TRUE ) next j  if( label i and label joverlap )  {   // Adjust the label priorities to make the evaluationfunction work properly.   // Note that the highest priority labels areassigned the lowest numbers and   // priorities may be positive ornegative.   adjusted_priority_1 = 1 + priority_range −             (label_1_priority − priority_of_most_important_label )  adjusted_priority_2 = 1 + priority_range −             (label_2_priority − priority_of_most_important_label )   collision_score= collision_score +          (adjusted_priority_1)*(adjusted_priority_1) +          (adjusted_priority_2)*(adjusted_priority_2)  }  next j next i// Halting Algorithm --------------------------------------- // is thereslow change ? if(collision_score <= previous_collision_score AND  collision_score > 0.98*previous_collision_score) {  slow_change_count= slow_change_count + 1 } else {  slow_change_count = 0 } // is thereoscillation ? if( (collision_score > previous_collision_score AND   previous_collision_score < previous_previous_collision_score ) OR  (collision_score < previous_collision_score AND   previous_collision_score > previous_previous_collision_score ) ) { oscillation_count = oscillation_count + 1 } else {  oscillation_count =0 } iteration_count = iteration_count + 1previous_previous_collision_score = previous_collision_scoreprevious_collision_score = collision_score if(collision_score = 0) gotoADJUST_LABEL_PARAMETERS if(iteration_count > 20) gotoADJUST_LABEL_PARAMETERS if(slow_change_count > 4) gotoADJUST_LABEL_PARAMETERS if(oscillation_count > 6) gotoADJUST_LABEL_PARAMETERS goto Start of Next IterationADJUST_LABEL_PARAMETERS: //-------------------------------------------// set label flag DRAW = TRUE for all labels for i = first label to lastlabel  label_i_DRAW = TRUE next i // these loops go thought labelpriority list and set the draw flag for i = first label to last label if( label i flag LABEL_TOO_MUCH_OUTSIDE_PORTRAIT = TRUE OR    label iflag LABEL_OUTSIDE_PORTRAIT = TRUE )  {  label_i_DRAW = FALSE  next i  } for j = label i+1 to last label  if( label j flagLABEL_TOO_MUCH_OUTSIDE_PORTRAIT = TRUE OR    label j flagLABEL_OUTSIDE_PORTRAIT = TRUE )  {   label_j_DRAW = FALSE   next j  } if( label i and label j overlap )  {   if ( label_i_MUST_DRAW = TRUEAND label_j_MUST_DRAW = TRUE )   {   label_j_DRAW = FALSE   }   else if( label_i_MUST_DRAW = TRUE )   {   label_j_DRAW = FALSE   }   else if (label_j_MUST_DRAW = TRUE )   {   label_i_DRAW = FALSE   }   else   {  label_j_DRAW = FALSE   }  }  next j next i return to caller

While the particular SYSTEM AND METHOD FOR LABELING MAPS as herein shownand described in detail is fully capable of attaining theabove-described objects of the invention, it is to be understood that itis the presently preferred embodiment of the present invention and isthus representative of the subject matter which is broadly contemplatedby the present invention, that the scope of the present invention fullyencompasses other embodiments which may become obvious to those skilledin the art, and that the scope of the present invention is accordinglyto be limited by nothing other than the appended claims, in whichreference to an element in the singular means “at least one”. Allstructural and functional equivalents to the elements of theabove-described preferred embodiment that are known or later come to beknown to those of ordinary skill in the art are expressly incorporatedherein by reference and are intended to be encompassed by the presentclaims. Moreover, it is not necessary for a device or method to addresseach and every problem sought to be solved by the present invention, forit to be encompassed by the present claims. Furthermore, no element,component, or method step in the present disclosure is intended to bededicated to the public regardless of whether the element, component, ormethod step is explicitly recited in the claims.

I claim:
 1. A method for generating a solution for pulling a label within a boundary of a map utilizing a computer system comprising the computer implemented steps of: determining, if the label is not wholly within the boundary of the map, a fraction of a label area that is inside the boundary of the map, moving the label within the boundary of the map if: a. the fraction of the label area inside the boundary of the map is greater than a predetermined value, b. a distance of a movement of the label is less than a maximum movement permitted from an original position, and c. the movement would result in all vertices located within the boundary of the map, and then outputting the solution to a caller, wherein a boundary of the label is a convex polygon with pre-assigned properties including the original position, the vertices, a type of movement allowed, and the maximum movement permitted from the original position, and wherein the boundary of the map is a rectangle.
 2. The method of claim 1 wherein the type of movement allowed is a vector type movement.
 3. The method of claim 1 wherein the type of movement allowed is a 2D type movement.
 4. The method of claim 1 further comprising a computer implemented step of discarding the label after attempting to move the label within the boundary of the map if the label is not wholly inside the boundary of the map.
 5. The method of claim 1 further comprising the computer implemented step of concluding that the label is wholly within the boundary of the map if all of the vertices are inside the map.
 6. The method of claim 1 wherein the determining, if the label is not wholly within the boundary of the map, the fraction of the label area that is inside the boundary of the map, comprises: circumscribing a rectangle around the boundary of the label, dividing the rectangle into a n by m grid of sub-rectangles, testing a centroid of each sub-rectangle to determine if the sub-rectangle centroid is inside the label, testing, if the centroid is inside the label, if the centroid is inside the boundary of the map, and dividing a number of centroids both inside the label and inside the boundary of the map by a number of centroids inside the label.
 7. The method of claim 1 further comprising discarding the label if the fraction of the label area inside the boundary of the map is less than a predetermined value; wherein the boundary of the map is fixed relative to features within the boundary of the map; wherein the boundary of the map is additionally fixed relative to the original position of the label; and wherein the features are not eliminated before the discarding.
 8. The method of claim 1 further comprising discarding the label unless the label is always at least partially within the boundary of the map.
 9. A method for generating a solution for pulling a label within a boundary of a map utilizing a computer system comprising the computer implemented steps of: determining, if the label is not wholly within the boundary of the map, a fraction of a label area that is inside the boundary of the map, moving the label within the boundary of the map if: a. the fraction of the label area inside the boundary of the map is greater than a predetermined value, b. a distance of a movement of the label is less than a maximum movement permitted from an original position, and c. the movement would result in all vertices located within the boundary of the map, and then outputting the solution to a caller, wherein a boundary of the label is defined by a convex polygon so that the polygon circumscribes the label, the label having pre-assigned properties including the original position, the vertices, a type of movement allowed, and the maximum movement permitted from the original position, and wherein the boundary of the map is a rectangle.
 10. The method of claim 9 wherein the type of movement allowed is a vector type movement.
 11. The method of claim 9 wherein the type of movement allowed is a 2D type movement.
 12. The method of claim 9 further comprising a computer implemented step of discarding the label after attempting to move the label within the boundary of the map if the label is not wholly inside the boundary of the map.
 13. The method of claim 9 further comprising the computer implemented step of concluding that the label is wholly within the boundary of the map if all of the vertices are inside the map.
 14. The method of claim 9 wherein the determining, if the label is not wholly within the boundary of the map, the fraction of the label area that is inside the boundary of the map, comprises: circumscribing a rectangle around the boundary of the label, dividing the rectangle into a n by m grid of sub-rectangles, testing a centroid of each sub-rectangle to determine if the sub-rectangle centroid is inside the label, testing, if the centroid is inside the label, if the centroid is inside the boundary of the map, and dividing a number of centroids both inside the label and inside the boundary of the map by a number of centroids inside the label.
 15. The method of claim 9 further comprising discarding the label if the fraction of the label area inside the boundary of the map is less than a predetermined value; wherein the boundary of the map is fixed relative to features within the boundary of the map; wherein the boundary of the map is additionally fixed relative to the original position of the label; and wherein the features are not eliminated before the discarding.
 16. The method of claim 9 further comprising discarding the label unless the label is always at least partially within the boundary of the map.
 17. A method for generating a solution for pulling a label within a boundary of a map utilizing a computer system comprising the computer implemented steps of: determining, if the label is not wholly within the boundary of the map, a fraction of a label area that is inside the boundary of the map, moving the label within the boundary of the map if: a. the fraction of the label area inside the boundary of the map is greater than a predetermined value, b. a distance of a movement of the label is less than a maximum movement permitted from an original position, and c. the movement would result in all vertices located within the boundary of the map, and then outputting the solution to a caller, wherein a boundary of the label is defined by a convex polygon so that the polygon circumscribes the label, the label having pre-assigned properties including the original position, the vertices, a type of movement allowed, and the maximum movement permitted from the original position, wherein the label is discarded unless the label in its original position is at least partially within the boundaries of the map, and wherein the boundary of the map is a rectangle.
 18. The method of claim 17 wherein the type of movement allowed is a vector type movement.
 19. The method of claim 17 wherein the type of movement allowed is a 2D type movement.
 20. The method of claim 17 further comprising a computer implemented step of discarding the label after attempting to move the label within the boundary of the map if the label is not wholly inside the boundary of the map.
 21. The method of claim 17 further comprising the computer implemented step of concluding that the label is wholly within the boundary of the map if all of the vertices are inside the map.
 22. The method of claim 17 wherein the determining, if the label is not wholly within the boundary of the map, the fraction of the label area that is inside the boundary of the map, comprises: circumscribing a rectangle around the boundary of the label, dividing the rectangle into a n by m grid of sub-rectangles, testing a centroid of each sub-rectangle to determine if the sub-rectangle centroid is inside the label, testing, if the centroid is inside the label, if the centroid is inside the boundary boundaries of the map, and dividing a number of centroids both inside the label and inside the boundary of the map by a number of centroids inside the label.
 23. The method of claim 17 further comprising discarding the label if the fraction of the label area inside the boundary of the map is less than a predetermined value; wherein the boundary of the map is fixed relative to features within the boundary of the map; wherein the boundary of the map is additionally fixed relative to the original position of the label; and wherein the features are not eliminated before the discarding. 